Crosstalk noise becomes one of the critical issues gating design closure for nano-meter designs. Pessimism in noise analysis can lead to significant additional time spent addressing false violations. Taking logic correlation into consideration, noise analysis can reduce pessimism significantly by eliminating false noise signals [1]-[3][5]-[7][10]-[13]. Eliminating the aggressors from the aggressor candidate set that can not switch simultaneously restricted by the logic exclusivity (LE) relationship among them can save simulation time as well. The LE problem, being proved as NP-complete, is basically to determine the subset (possibly multiple equivalent subsets) of a given aggressor candidate set which has the largest combined weight out of all possible subsets governed by logic exclusivity constraints. This paper presents a new approach in resolving the LE problem, which employs a gain guided backtrack search technique that does not require exhaustive search of all the binary paths to reach an optimal solution. We first prove that under certain conditions, if the gain at each level is non-negative, then the result will be optimal. Based on this theorem, a new algorithm is developed. The experimental results demonstrate the efficiency and accuracy of this approach. The algorithm can quickly find the optimal solutions for most cases from industry designs and outperforms other methods.

To make the application of the finite-element method practical in semiconductor device simulation, the authors have applied the Scharfetter-Gummel (S-G) scheme in conjunction with an accurate seven-point Gaussian quadrature rule to the assembly of the finite-element stiffness matrices and the right-hand-side vector of the semiconductor equations. The key of this method lies in accurate interpolation rules, which are derived on the basis of simple device physics considerations. The inherent simplicity and flexibility in the finite element formulation make the new method applicable to multidimensional problems. The simplicity of embedding the S-G scheme in the quadrature of finite-element assembly lends itself to all kinds of finite-element methods using various elements, shape functions, and weightings. The resultant exponential functional fitting avoids high discretization errors usually incurred by the classical finite-element discretization method. Solutions with high accuracy, even on coarse mesh, and a significant speed-up of convergence rate are obtained.>

POSM (pseudo-objective function substitution method), is an unconstrained optimization algorithm. This algorithm, requiring neither derivative calculation nor linear search step, substitutes the objective function by a second-order approximated formulation, enhancing the convergence rate substantially and implemented in the general-purpose Analysis and Design Program for Integrated Circuits, (ADIC-2.C). To show the effectiveness and efficiency of this algorithm, it was evaluated using a number of numerical examples and some practical IC designs.>